Taking the serpentine route

The ins and outs of a
serpentine belt drive
design are revealed in
this application where
synchronous belting
replaces gears.

Jack Zedek, Rockwell Automation | Nov 01, 2000

Synchronous belts are often used instead of flat or v belts for several reasons, the most notable being the near-perfect shaft synchronization they provide. They remain in mesh with their sprockets, while traction-based belts on pulleys can slip.

Synchronous belts are a popular choice for serpentine drives, in which a single belt turns three or more pulleys or sprockets. Besides providing zero-slip, synchronous belts allow a little more “aggressive” belt geometry – the toothed belt can often move the sprocket with a shorter arc of contact than a flat belt along a pulley, and this additional freedom makes complex serpentine arrangements easier to design. Even with toothed belts, however, serpentine configurations often require special attention. For instance, shafts sometimes rotate in opposite directions, in which case a two-sided synchronous belt is required.

The following is an example of serpentine synchronous belt drive design. The machinery involved is a press roll system with two contacting rollers of opposing rotation. The original configuration uses a motor connected to a gearbox, with a spur pinion mounted to the gearbox output shaft. This external pinion meshes with a larger gear attached to one of the rolls. The gear then drives a second identical gear and roller in the other direction. The goal is to replace all external gearing with belts to eliminate the maintenance and excessive noise.

Before selecting the belt, sprockets, and bushings for such an application, the following should be established: XY coordinates of each shaft centerline (with respect to any convenient datum); necessary horsepower for each shaft; the overall horsepower requirement; speed of each shaft; a description of each shaft’s function (type of equipment attached); and knowledge of shock loads and environmental conditions.

In the press roll system, motor speed is 1,750 rpm. The motor puts out 7.5 hp and is mounted to a gearbox with a 20.9:1 reduction. The two larger external gears have 30 teeth, attaching to a 2 7/16 -in. shaft. The 18-tooth pinion attaches to a 1 3/8 -in. shaft. All shafts are aligned, with center distances of 9.55 and 21.45 in. from the pinion to each of the two gears. All of the shafting is there to stay; it cannot be moved or changed. Some level of shock loading is expected.

Knowing the motor and gearbox specs, we could base our design on the maximum driving power. But, even better, the user provides the required power: each roll needs 2.5 hp to operate. Typical service factors for serpentine drives are no less than 2.0, but because of shock loading and relatively tight drive geometry, we choose a slightly more conservative service factor of 2.2.

We use the value of 5 hp (two rolls requiring 2.5 hp apiece) for the system horsepower; this driven horsepower, if known, is preferred over the driving (motor) horsepower. System efficiency is therefore irrelevant because the rolls require 100% of the specified driven power. If, on the other hand, our belt selection were based on motor horsepower, gearbox efficiency would be factored in. If unknown, it would be reasonable to assume a conservative (in this case, deliberately large) efficiency value – the greater the efficiency in the equation, the higher the design horsepower.

With a system horsepower of 5, a safety factor of 2.2, and an efficiency of 1, we have a design horsepower of 11. The belting and driving sprocket must be capable of transmitting 11 hp at the gearbox output speed of 84 rpm. To match the operation of the original system, this output speed must be further reduced by the 30:18 (1.66) reduction ratio of the pinion and gears that are being replaced.

Sprocket designation is a good place to begin. This involves the belt width, tooth pitch, and pitch diameter, parameters associated with horsepower, speed, and space requirements. Based on the speed and horsepower, a 14-mm HTD is the first pitch choice. HTD, or High Torque Drive, has become the baseline rating for power belts. Specs like HT150 refer to a rating that’s 150% of the baseline. “HTD” can therefore also be written “HT100.”

Using the 14-mm HTD sprocket as our launch pad, we go to any standard (HTD-based) ratio and center-distance tables corresponding to 14-mm pitch. A 68 to 112 combination (1.65 reduction ratio) is available at the specified pitch, but doesn’t fit in the 9.55-in. center distance between the driving and the first driven sprocket. A smaller sprocket combination of 38 to 64 is then used, providing a 1.68 reduction ratio.

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Had it fit, the bigger sprocket combination would have been better. Largerdiameter sprockets allow a narrower belt width. With a narrower belt, the transverse load can be forced axially closer to the bearing, thus reducing moment loading. But larger sprockets would have meant moving the shafts further apart and increasing the roll diameter.

The width of the belt is then specified. For these 38 and 64-tooth, 14-mm HTD sprockets, a 115-mm wide belt carries 11.8 hp at 84 rpm. This selection acceptably increases the service factor to 2.36.

To determine belt path geometry, a graphical approach can be used, using either CAD software or engineering paper. One of the criteria for HTD synchronous belting is that the contact arc be at least 60° with no less than six teeth in mesh. Furthermore, it’s best to place the idler on the slack side of the belt (belt direction from driving to idler sprocket). Center distances are fixed for all shafting except the idler, and the working sprockets are already designated. Thus, idler selection and placement are the free parameters.

For our scale drawing we use an idler the same size as the driving sprocket. While there is no apparent reason to go larger than this, using an idler smaller than the smallest working sprocket will generally detract from belt life. However, other constraints may take precedence, and deviation from this guideline is sometimes necessary.

As for idler location, it can be somewhat arbitrarily placed along the Y axis, parallel to the line joining the three working sprockets’ centers. Shifting the idler on this axis will only affect the angle of contact with the two outer working sprockets, and with the geometry that’s in place, these contact angles are likely to remain high regardless. The idler’s distance along the X axis is what matters. This is the take-up distance – it’s what compensates for belt slack.

To determine belt size, dimension all arcs and tangent lines (a lot easier with CAD) and vary the take-up distance within a reasonable window so that total length can be matched to a stock belt size. With the system described here, a 246-mm (9.7-in.) take-up distance allows a 2,230-mm stock belt. At this location, the idler sprocket still maintains 81° of belt contact. The next closest stock belt is 2,310 mm, which would require moving the idler further away from the system. In our case this is unnecessary, even undesirable. So, the take-up distance is set at 9.7 in.

While flat-faced idler pulleys are sometimes used with the flat side of a single- sided synchronous belt, this belt is double-sided and requires a toothed idler sprocket.

(circumference, pitch, width [all mm]) Working sprockets are fixed to the shafts with high-friction bushings so the sprocket and shaft turn together. However, the idler sprocket needs an antifriction bearing, as it rides on a static axle. This bearing is selected or designed according to the required size (the idler has a 3020 bushing size), speed, and loading. It may happen that an antifriction bearing isn’t readily obtainable in the required size, and to avoid delay the designer may consider decreasing the idler sprocket diameter for compatibility with an available bearing. This is generally reasonable, if not ideal.